detailed information: The input equation set is: Question solving process:
Multiply both sides of equation (1) by 25 Divide the two sides of equation (1) by 16, the equation can be obtained: | | 100 | x | + | | | 25 2 | y | + | | | 25 16 | z | = | | | 1025 8 | (4) | , then subtract both sides of equation (4) from both sides of equation (2), the equations are reduced to:
| | | | - | 5 2 | y | | - | 9 16 | z | = | | - | 545 8 | | (2) |
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Divide the two sides of equation (1) by 64, the equation can be obtained: | | x | + | | | 1 8 | y | + | | | 1 64 | z | = | | | 41 32 | (5) | , then subtract both sides of equation (5) from both sides of equation (3), the equations are reduced to:
| | | | - | 5 2 | y | | - | 9 16 | z | = | | - | 545 8 | | (2) |
| | | 319 8 | y | | - | 1 64 | z | = | | - | 41 32 | | (3) |
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Multiply both sides of equation (2) by 319 Divide the two sides of equation (2) by 20, the equation can be obtained: | - | 319 8 | y | | - | 2871 320 | z | = | | - | 34771 32 | (6) | , then add the two sides of equation (6) to both sides of equation (3), the equations are reduced to:
| | | | - | 5 2 | y | | - | 9 16 | z | = | | - | 545 8 | | (2) |
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Multiply both sides of equation (3) by 45 Divide both sides of equation (3) by 719, get the equation: | - | 6471 11504 | z | = | | - | 391635 5752 | (7) | , then subtract both sides of equation (7) from both sides of equation (2), get the equation:
Multiply both sides of equation (3) by 80 Divide both sides of equation (3) by 719, get the equation: | - | 719 719 | z | = | | - | 87030 719 | (8) | , then add the two sides of equation (8) to both sides of equation (1), get the equation:
| | | | 64 | x | + | | 8 | y | = | | - | 28072 719 | | (1) |
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Multiply both sides of equation (2) by 16 Divide both sides of equation (2) by 5, get the equation:, then add the two sides of equation (9) to both sides of equation (1), get the equation:
The coefficient of the unknown number is reduced to 1, and the equations are reduced to:
Therefore, the solution of the equation set is:
Convert the solution of the equation set to decimals:
解方程组的详细方法请参阅:《多元一次方程组的解法》 |